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March 14th, 2015, 10:16 PM   #1
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Confidence Interval -- conceptual understanding

In a randomly selected sample of 500 registered voters in Kowloon, 200 individuals say that they plan to vote for Candidate A in the upcoming election.

- If the survey were repeated a lot of times, we expect 90% of the confidence intervals constructed will contain the proportion of all Kowloon voters who plan to vote for Candidate A.

- If the survey were repeated a lot of times, we expect 90% of the confidence intervals constructed will contain 40%, which is the estimate of the proportion of Kowloon voters who vote for Candidate A.

I think the second statement is right, but I was wrong. Why? What's the difference between the two?
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March 15th, 2015, 01:49 PM   #2
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40% is an estimate of the proportion, but it is not necessarily the true proportion.
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March 15th, 2015, 08:27 PM   #3
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Does that mean when we do the survey many times, it is expected that the intervals we get will be the true proportion?
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March 16th, 2015, 03:52 PM   #4
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One of the basic theorems in probability theory is the law of large numbers, which says (essentially) that a sample average converges to the mean as the sample size gets bigger.
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